I use mostly the Lounge and General Discussion. I do venture to some of the others, but not so much lately. There has been an abundance of posts on GD and it pretty much take up all my viewing time to get through the 3-4 or some days, 4-5 pages of new posts.
I too hate anything that shows animal mistreatment. However, I can't say I have seen any animal torture or mistreatment in either of the forums I read.
Yes, there will be stories of abused and abandoned animals but those are ones that end up having a happy ending. DU'ers are not in the habit of posting nasty, gruesome articles of any subject just to post disgusting stuff.
So not sure where you are seeing these "graphic, gruesome animal torture stories". I may have missed them. 
Please report them when you do come across them. No one should have to even accidently see mistreatment of animals.
Do not post content that is Not Safe For Work (NSFW), which includes sexually explicit material, graphic depictions of bodily functions, or images of extreme violence, gore, pain, or human suffering. Exceptions are permitted when an image adds important context to a legitimate news story, but the post must include a "graphic content warning" in the subject line.
Why we have this rule: Most people do not enjoy stumbling across extremely graphic content while browsing the web.
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